Polytope of Type {5,10} with group SmallGroup(1440,5843)

Overview

Group: SmallGroup(1440,5843)
Rank: 3
Schläfli Type: {5,10}
Vertices, edges, …: 72, 360, 144
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{5,5}*720

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*(s1*s2)^2*(s1*s0)^2*s2*s1*s2> of order 3

48 facets

48 of {5}*10

24 vertex figures

24 of {10}*20

P/N, where N=<s0*(s1*s2)^2*(s1*s0)^2*s2*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 9

16 facets

16 of {5}*10

8 vertex figures

8 of {10}*20

Representations

Permutation Representation (GAP)

s0 := ( 1, 3)( 2, 6)( 4, 9)( 5, 7)( 8,10);;
s1 := ( 1, 2)( 3, 4)( 5,10)( 6, 7)( 8, 9);;
s2 := ( 1, 7)( 2,10)( 3, 5)( 4, 9)( 6, 8)(11,12);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(12)!( 1, 3)( 2, 6)( 4, 9)( 5, 7)( 8,10);
s1 := Sym(12)!( 1, 2)( 3, 4)( 5,10)( 6, 7)( 8, 9);
s2 := Sym(12)!( 1, 7)( 2,10)( 3, 5)( 4, 9)( 6, 8)(11,12);
poly := sub<Sym(12)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;

References

None.

to this polytope.